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Resonant Inelastic X-Ray Scattering at the
Oxygen K Resonance of NiO: Nonlocal Charge
Transfer and Double-Singlet Excitations
L.-C. Duda, T. Schmitt, Martin Magnuson, J. Forsberg, A. Olsson,
J. Nordgren, K. Okada and A. Kotani
N.B.: When citing this work, cite the original article.
Original Publication:
L.-C. Duda, T. Schmitt, Martin Magnuson, J. Forsberg, A. Olsson, J. Nordgren, K. Okada
and A. Kotani, Resonant Inelastic X-Ray Scattering at the Oxygen K Resonance of NiO:
Nonlocal Charge Transfer and Double-Singlet Excitations, 2006, Physical Review Letters,
(96), 067402.
http://dx.doi.org/10.1103/PhysRevLett.96.067402
Copyright: American Physical Society
http://www.aps.org/
Postprint available at: Linköping University Electronic Press
http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-17408
Resonant Inelastic X-Ray Scattering at the Oxygen K Resonance of NiO:
Nonlocal Charge Transfer and Double-Singlet Excitations
L.-C. Duda, T. Schmitt,* M. Magnuson, J. Forsberg, A. Olsson, and J. Nordgren
Department of Physics, Uppsala University, P.O. Box 530, S-751 21 Uppsala, Sweden
K. Okada1and A. Kotani2,3
1The Graduate School of Natural Science and Technology, Okayama University, Okayama 700-8530, Japan 2RIKEN/Spring8,1-1-1 Kouto, Mikazuki-cho, Saya-gun, Hyogo 679-5148, Japan
3Photon Factory, IMSS, High Energy Accelerator Research Organization, 1-1 Oho Tsukuba, Ibaragi 305-0801, Japan (Received 7 July 2005; published 16 February 2006)
We report high-resolution polarization-dependent resonant inelastic x-ray scattering (RIXS) at the O K resonance of NiO showing a rich excitation spectrum. We perform multisite Ni6O19cluster model cal-culations, revealing that solid state effects are substantial. We identify a nonlocal charge transfer exci-tation at 4 –5 eV and double-singlet creation at 1.75 eV, both exhibiting significant scattering geometry dependence. Apart from an intense band of local charge transfer excitations (above 5 eV) also dd exci-tations at 1 eV are observed. Finally, we point out that O K RIXS of correlated metal oxides allows a quan-titative and consistent determination of the charge transfer energy and the Hund coupling energy JH. DOI:10.1103/PhysRevLett.96.067402 PACS numbers: 78.70.En, 71.15.m, 71.27.+a
NiO is one of the prototypical compounds that has high-lighted the importance of correlation effects in transition metal oxides. However, despite several decades of studies there is still no literature consensus on the detailed elec-tronic structure of NiO [1]. Although exhibiting a partially filled 3d band and predicted by simple band theory to be a good conductor, NiO has a relatively large band gap (de-termined to be about 4 eV by optical measurements) that cannot be accounted for in the otherwise successful local density approximation calculations. Even taking magnetic interactions into account, band theory fails to explain the magnitude of the gap satisfactorily. Relying on a combi-nation of two separate electron spectroscopies, Sawatzky and Allen [2] found a (conductivity) gap of 4.3 eV between the onsets of photoelectron spectra (PES) and inverse photoelectron spectra (IPES). The lowest energy states were assigned to d8L(PES) and d9 (IPES). On the other
hand, the correlation gap is defined as the energy for transferring electrons between two Ni sites (Coulomb en-ergy), which is considerably higher (7– 9 eV). Also core level spectroscopies bear evidence for the highly correlated nature of low-energy excitations. For instance, the asym-metry of the Ni 2p line shape has been attributed to non-local charge transfer excitations and multisite cluster calculations show that solid state effects generally are appreciable for correlated materials, such as cuprates and high Tccompounds [3].
In the face of the fact that much of our experimental knowledge about the electronic structure of NiO is based upon combined electron spectroscopies, it is timely to ap-ply a single charge neutral spectroscopic probe. Resonant inelastic x-ray scattering (RIXS) is a photon-only tech-nique performed at soft x-ray absorption resonances mak-ing it atomically sensitive, orbital symmetry specific, and bulk sensitive and thus complementary in many respects
to electron spectroscopy. RIXS is a powerful probe for studying correlated materials and has been described in recent literature [4 –8]. In RIXS, the energy loss between the incoming and scattered photons are recorded and cor-respond to the energies of charge neutral low-energy ex-citations which obey the selection rule l 0; 2. In RIXS of correlated oxides local crystal field excitations (which are difficult to observe by other techniques [9]) of the type d8(dd excitations) and d9L(local charge
trans-fer excitation) are prominent. Moreover, for cuprates it has been shown that O K RIXS allows the observation of
nonlocal (Zhang-Rice-like) excitations in certain detection
geometries [6]. It would be equally interesting and chal-lenging to be able to study similar excitations in the RIXS of NiO.
In this Letter, we present results from high-resolution polarization-dependent RIXS experiments at the O K reso-nance of NiO and compare to cluster model calculations using a Ni6O19cluster shown in Fig. 1. We observe, apart
from the main band with a high energy shoulder (HES), previously undetected dd and double-singlet excitations. Previous, lower resolution, studies of NiO using RIXS-related techniques at the Ni L edge [10] and at the O K edge [11,12] either did not reveal the full low-energy excitation spectrum or the analysis was based on band structure calculations which are less appropriate for dis-cussing specific excitations. In contrast, our combination of high energy resolution and polarization-dependent RIXS together with advanced multisite cluster model cal-culations reveals a rich low-energy excitation spectrum and its connection with the strongly correlated nature of NiO. First, we clarify the origin of known NiO-specific features such as the HES which is found to be due to nonlocal charge transfer (NLCT). Second, our study shows more generally that RIXS is also a powerful probe for investigat-0031-9007= 06=96(6)=067402(4)$23.00 067402-1 © 2006 The American Physical Society
ing nonlocal magnetic excitations such as double-singlet creation (DSC) states.
The O K-RIXS measurements have been performed at beam line I511–3 at MAX II (MAXLAB National Laboratory, Lund University, Sweden), based on a modi-fied SX-700 monochromator layout [13]. The detection system was a grazing incidence grating spectrometer in the Rowland geometry [14]. For detecting the O K-RIXS spectra we used the following spectrometer configuration: 1200 lines=mm, 5 m grating in first order of diffraction. The spectrometer resolution was set to about 0.5 eV and the monochromator spectral band width was chosen to have a somewhat smaller value. We used a commercially obtained large single crystal NiO as well as powder samples (with consistent results). All data were taken with the samples at room temperature. The emission energy scale was obtained by recording the Zn L;emission from a pure Zn foil and
the Na K emission from a fresh single crystal of NaCl and using the tabulated wavelengths from literature [15]. The monochromator energy calibration was done by comparing the NiO O K-absorption resonances with literature values [16].
The upper panel of Fig. 2 shows an O K-absorption scan where the lettered arrows indicate the respective excitation energies for the RIXS spectra. The lower panel of Fig. 2 shows the O K-RIXS emission spectra excited (A) on the maximum of the first O K resonance and (B) at 0.5 eV below the maximum on an energy loss scale. When tuning the x-ray energy to the first NiO O K-absorption peak, the O 1s electron is excited into empty O 2p states strongly hybridized with the Ni 3d states. Two different detection geometries are compared: depolarized (polarized) geome-try means that the scattered x rays are detected along (perpendicular to) the direction of the electric field vector of the incident x rays [17].
The spectra in Fig. 2 are dominated by an intense broad peak (maximum about 7 eV energy loss) with a high energy shoulder (4 –5 eV energy loss). This is consistent with previous observations [11,18], and here we record the elastic peak energy which allows the determination of the corresponding loss energies. Moreover, we observe
exci-tations at lower energies (<2 eV), which are shown in detail in the inset of Fig. 2. The main contribution is attributed to dd excitations at about 1 eV which are medi-ated by the O 1s-core hole state. This means that d8final
states of the excited Ni ion are reached, where the asterisk denotes configurations that deviate from the ground state. The dd excitations of NiO have been observed in Ni
L-edge RIXS [10] with the strongest component at 1 eV energy loss, which is corroborated by Ni M-edge RIXS at much higher resolution. Note also the extra intensity at about 1.75 eV energy loss that is observed in the polarized geometry but absent in the depolarized geometry. We will discuss the origin of this feature below.
Although some aspects of the NiO O K x-ray emission spectra can be described using a band theoretical approach, we recall that it has been found experimentally [5] and has been described theoretically [19] that O K spectra of cor-related materials also can exhibit many-body features that have no counterpart in one electron theory. Figure 3 shows the theoretical RIXS spectra Smncalculated at the central O site of the Ni6O19 cluster model, where m (n) represents that the polarization vector of the emitted (incident) x ray is parallel to the m (n) axis. The depolarized spectrum is proportional to Szx, while the polarized one is proportional to the average of Sxxand Szx. These spectra are calculated
)s ti n u . br a( yti s ne t nI -10 -5 0
Energy Loss (eV) 1.75 eV 0.8 eV 4.5 eV NiO O1s-RIXS depolarized polarized
A
B
-3 -2 -1 0 1Energy Loss (eV)
DSC dd n oit pr os b A 550 540 530
Incident x-ray energy
A B
NiO O1s-absorption
NLCT A
FIG. 2 (color online). Top panel: O K absorption of NiO. The lettered arrows mark the chosen excitation energies for the RIXS spectra. Bottom panel: O K RIXS at the first absorption reso-nance of NiO (A) and 0.5 eV below (B). The inset gives a magnified view of the excitations below the NLCT energy of spectra at excitation energy A (the heavy lines represent a three-point average of the data).
FIG. 1. A schematic perspective view of the Ni6O19 cluster used for our calculations. The black circles represent Ni-ion sites and the white and gray circles represent O-ion sites.
using the Kramers-Heisenberg formula, taking into ac-count the geometrical arrangement and the incident and scattered photon polarization of the present experiment.
In our Ni6O19cluster model, the center of the cluster is the O site and it is surrounded with six NiO6units (Fig. 1). We assume that the central O atom is excited by an x-ray photon. If the electric field of the x ray is x polarized, the O 2pxhole on the central O site, which is strongly hybridized
with Ni 3d states, is annihilated in the intermediate state. In the depolarized geometry, an O 2pyor O 2pzelectron fills the O 1s core hole in the subsequent x-ray emission pro-cess. The resultant O 2py(O 2pz) hole may hybridize with the Ni 3d states. Thus the Ni-to-Ni charge transfer (CT) occurs via the O 1s core hole state. The present Ni6O19is
the minimum size cluster that accounts for the NLCT but the full exact-diagonalization calculation for this cluster model is presently too computer intensive. For simplicity, we disregard the Ni-to-Ni CT path via the gray O sites shown in Fig. 1. In order to concentrate on the charge transfer excitations, we restrict the basis atomic wave functions that describe the Hamiltonian to O 2px;y;z and
Ni 3dx2y2;3z2r2[20] and the multiplet coupling effects (dd
excitations) are disregarded for simplicity. The diagonal matrix elements of the Hamiltonian are described with the charge transfer energy between Ni 3d and O 2p states ( 3:8 eV), the on-site Coulomb repulsion (Udd 7:2 eV) and Hund coupling on Ni sites (JH 1:3 eV). The off-diagonal matrix elements are described with the
pd hybridization strength [Veg 2:2 eV] and the pp hybridization strength (tpp 0:3 eV).
We find that the spectrum for the depolarized geometry (proportional to Szx) consists of four structures (Fig. 3). Feature P1 at 11 eV is due to d10L2. Feature P2 at
7:5 eV is caused by CT to the antibonding state between
d9Land d8. Feature P3 at 6:3 eV can be assigned to the
nonbonding type d9Lin the single-site model. Compared
to experiment, the features P2 and P3 in Fig. 3 are found at somewhat smaller energy loss and the intensity of P2 has too much spectral weight. This is partly because the Ni 3dt2g orbitals are disregarded in the calculation and
partly because the cluster size is still too small.
Feature P4 at 4:1 eV is a state split off from the nonbonding type d9L due to NLCT excitation, i.e., an
excitation involving two Ni sites: jd9; d8Li. This is the
RIXS analog to the state described by van Veenendaal and Sawatzky in the Ni 2p x-ray photoelectron spectrum (XPS) of NiO [3]. In the Ni 2p XPS spectrum, nonlocal excitations lead to a high binding-energy shoulder due to screening of the 2p core hole by an electron (2p3d9) from
a neighboring NiO6 unit. The energy difference between the unscreened and this screened state is about 2 eV. By contrast, the final state of RIXS has no core hole and we can measure the excitation energy of the jd9; d8Li NLCT state directly.
The NLCT defines the CT excitation edge and its energy loss is intimately related to the charge transfer parameter
, which makes the largest contribution to the
superex-change coupling constant J in NiO [21]. However, the
literature estimations for the value of , based on more indirect determination, spans a wide range from 2.0 to 6.5 eV [22]. Experimentally, we observe the charge trans-fer excitation edge at 4.5 eV, which is in good agreement with our cluster model calculation where we use the charge transfer energy parameter value 3:8 eV.
The corresponding structures P1–P4 can also be found in the spectrum for the polarized geometry (proportional to
Sxx Szx). This indicates that the overall polarization
dependence of O K RIXS in NiO is weak due to the high symmetry in the electronic state of the cluster. On the other hand, we find an extra peak P5 at 1:9 eV in Sxx (forbid-den in Szx). This loss energy is roughly twice the intra-atomic exchange interaction strength (Hund coupling en-ergy JH), which indicates that the peak is caused by a DSC
excitation [23]. Local spin-flip excitations have been pre-dicted earlier for RIXS at the L and M edges of Cu2and
Ni2 [24]. In that case a single spin-flip leads to an loss
peak at relatively low energy, which is presently difficult to resolve instrumentally [25]. In contrast, the DSC excitation is a nonlocal type excitation that occurs as a result of exchanging two holes between neighboring Ni sites. Suppose that j""; ##i denotes antiferromagnetically aligned spins of two holes on neighboring Ni sites, where " and # represent the spin state of each hole. When a " hole is transferred from the left Ni site to the right, and a # hole is transferred from the right to the left, j"#; "#i is realized. In other words, a double-singlet state is created as a result of double intersite CT. The DSC excitation energy is charac-terized by 2JH, albeit offset by about 0.7 eV due to the hybridization energy present in NiO.
We also briefly discuss the changes in the spectra when detuning from the first absorption resonance.
Experiment-Intensity [arb. units]
-12.5 -10.0 -7.5 -5.0 -2.5 0.0
Raman shift [eV]
P1 P2 P3 P4 P5 depolarized ∝ Szx polarized ∝ Sxx+Szx NiO O1s-RIXS cluster model calculation
Sxx
Szx
FIG. 3 (color online). The line spectra at the bottom show the polarized RIXS components Sxx and Szx. The curves represent the theoretical O K-RIXS spectra for NiO in the depolarized ge-ometry and the polarized gege-ometry as labeled. We applied a vari-able final state lifetime broadening and a Gaussian broadening to simulate the instrumental resolution of the RIXS spectra.
ally we observe that the dd excitations in spectrum B (Fig. 2) become strongly enhanced relative to the other ex-citations, in particular, in the polarized geometry. Detuning in RIXS leads to a faster scattering, suppressing processes taking more time [26]. Thus it is plausible that the nonlocal excitations or changes of x-ray polarization require more scattering time than the local dd excitations.
When tuning to energies higher than the first absorption maximum (not shown) the HES moves to about 0.4 eV higher energy. First, the excitation is less selective allowing many more intermediate states leading to a broader appear-ance of the spectrum. Second, the scattered photon energy no longer reflects the energy difference between the initial and final state since the delocalized excited electron re-moves part of the atomic energy. Instead, the photon energy is a measure of the energy between the intermediate and the final state which is an ionized state similar to a photoemission final state. Thus the nonresonantly excited location of the HES corresponds very closely to the
d8L-photoemission peak with the lowest binding energy
at about 2 eV [2,27].
In conclusion, we find that O K-RIXS spectra excited close to the K-absorption threshold reflects the energy loss of charge neutral excitations. We perform a multisite clus-ter calculation and find very good agreement with the salient features of the experimental O K-RIXS spectra. Using parameter values 3:8 eV for the charge transfer energy and Udd 7:2 eV for the Coulomb repulsion cor-roborates the placement of NiO in the charge transfer regime of the Zaanen-Sawatzky-Allen diagram [28].
In the O K RIXS of NiO we assign the resonant high energy shoulder at 4.5 eV to nonlocal charge transfer excitations and a highly anisotropic feature, found experi-mentally at 1.75 eV energy loss, to double spin flip crea-tion. This excitation is only visible in the RIXS spectrum observed in the polarized geometry, exactly as predicted in our calculations. The nonlocal DSC excitation is a unique and sensitive probe for determining Hund’s exchange en-ergy JH and the influence of covalency effects.
Our results demonstrate that solid state effects of corre-lated oxides can be identified and the corresponding ener-gies can be accurately determined by combining O
K-RIXS experiments and multisite cluster calculations. Future higher resolution studies of NiO O K RIXS and other correlated materials, will most likely reveal excita-tions at even lower loss energies (e.g., the two-magnon excitation) and provide theoretical challenges for including collective excitations in model calculations.
This work was supported by the Swedish Research Council (VR) and the Go¨ran Gustafsson Foundation (GGS) and by a Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology (Japan). The experimental work was per-formed at MAXLAB in Lund (Sweden). We thank G. Dra¨ger for providing us with the single crystal sample. We gratefully acknowledge the MAXLAB staff for excel-lent support and working conditions at the beam line.
*Permanent address: Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland.
[1] Landolt-Bo¨rnstein-Group III Condensed Matter
(Springer-Verlag, GmbH, 2000), Vol. 41.
[2] G. A. Sawatzky and J. W. Allen, Phys. Rev. Lett. 53, 2339 (1984).
[3] M. A. van Veenendaal and G. A. Sawatzky, Phys. Rev. Lett. 70, 2459 (1993).
[4] P. Kuiper et al., Phys. Rev. Lett. 80, 5204 (1998). [5] L.-C. Duda et al., Phys. Rev. B 61, 4186 (2000). [6] Y. Harada et al., Phys. Rev. B 66, 165104 (2002). [7] A. Kotani and S. Shin, Rev. Mod. Phys. 73, 203 (2001). [8] L.-C. Duda et al., Phys. Rev. Lett. 93, 169701 (2004). [9] R. J. Powell and W. E. Spicer, Phys. Rev. B 2, 2182
(1970).
[10] M. Magnuson et al., J. Phys. Condens. Matter 14, 3669 (2002).
[11] V. I. Anisimov, P. Kuiper, and J. Nordgren, Phys. Rev. B
50, 8257 (1994).
[12] T. M. Schuler et al., Phys. Rev. B 71, 115113 (2005). [13] R. Denecke et al., J. Electron Spectrosc. Relat. Phenom.
101–103, 971 (1999).
[14] J. Nordgren et al., Rev. Sci. Instrum. 60, 1690 (1989). [15] J. A. Bearden, Rev. Mod. Phys. 39, 78 (1967). [16] F. M. F. de Groot, Phys. Rev. B 40, 5715 (1989). [17] M. Matsubara et al., J. Phys. Soc. Jpn. 69, 1558 (2000). [18] N. Wassdahl et al., in X-ray Inner Shell Processes,
Proceedings of the X-90 Conference, edited by T. A.
Carlson, M. O. Krause, and S. T. Manson, AIP Conf. Proc. No. 215 (AIP, New York, 1990), p. 451– 464. [19] K. Okada and A. Kotani, J. Phys. Soc. Jpn. 72, 797
(2003).
[20] K. Okada, J. Phys. Soc. Jpn. 73, 1681 (2004).
[21] M. A. van Veenendaal et al., Phys. Rev. B 51, 13 966 (1995).
[22] 6.2 eV: J. van Elp et al., Phys. Rev. B 45, 1612 (1992); S. Hu¨fner, Adv. Phys. 43, 183 (1994); M. A. van Veenendaal et al., Phys. Rev. B 51, 13 966 (1995); 5 eV: M. Takahashi and J. Igarashi, Phys. Rev. B 54, 13 566 (1996); 4.7 eV: T. Jo and A. Tanaka, J. Electron Spectrosc. Relat. Phenom. 117, 397 (2001); 3.5 eV: M. Magnuson
et al., J. Phys. Condens. Matter 14, 3669 (2002); 2.0 eV: A.
Kotani and K. Okada, Recent Advances in Magnetism of
Transition Metal Compounds, edited by A. Kotani and
N. Suzuki (World Scientific, Singapore, 1993), p. 12. [23] Note that contributions from dd excitations at similar
energies [B. Fromme et al., Phys. Rev. Lett. 75, 693 (1995)] are nearly isotropic and less intense than the contribution from the DSC peak observed in our O
K-RIXS spectra.
[24] F. M. F. de Groot, P. Kuiper, and G. A. Sawatzky, Phys. Rev. B 57, 14 584 (1998).
[25] After submission of our manuscript a study on M-edge RIXS of NiO was published, showing evidence of a local spin-flip excitation: S. G. Chiuzbaian et al. Phys. Rev. Lett. 95, 197402 (2005).
[26] F. K. Gelmukhanov and H. A˚ gren, Appl. Phys. A 65, 123 (1997).
[27] M. Portalupi et al., Phys. Rev. B 64, 165402 (2001). [28] J. Zaanen, G. A. Sawatzky, and J. W. Allen, Phys. Rev.
Lett. 55, 418 (1985).
